Fortunately, the argument is the same in all three cases. Let h denote the length of this line AD, that is, the height or altitude of the triangle. But this is true even when B is an obtuse angle as in the third diagram. There, angle ABC is obtuse. But the sine of an obtuse angle is the same as the sine of its supplement. These two equations tell us that h equals both c sin B and b sin C.
Since the three verions differ only in the labelling of the triangle, it is enough to verify one just one of them. In case 2, angle C will be a right angle. Example 1: Given two angles and a non-included side AAS. Find the remaining angle and sides. If two sides and an angle opposite one of them are given, three possibilities can occur. Consider a triangle in which you are given a , b and A.
Example 1: No Solution Exists. Find the other angles and side. So it appears that there is no solution. Verify this using the Law of Sines. Therefore, no triangle exists. Then we can use this ratio to find other sides and angles using the other givens.
Example In the figure below, we are given side b and angle B, which opposite each other, so we can use them to calculate the 'Law of Sines' ratio s for this particular triangle: Notice here we are also given the length of side c. So, because we know the Law of Sines ratio for this triangle s - Home Contact About Subject Index.
In any triangle, the ratio of a side length to the sine of its opposite angle is the same for all three sides. As a formula:.
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